Static and Kinetic Friction, Normals, Equilibrium and Accelerated Motion 1. A baseball player slides into home base with an initial speed of 7.90 m/s. If the coefficient of kinetic friction between the player and the ground is 0.41, how far will the player slide before coming to rest? 4. When you push a 1.80-kg book resting on a tabletop, it takes a force of 2.25 N to start the book sliding. Once it is sliding, however, it takes only a 1.50 N to keep the book moving with constant speed. What are the coefficients of static and kinetic friction between the book and the tabletop? 7. To move a large crate across a rough floor, you push down on it at an angle of 21, as shown below. Find the force necessary to start the crate moving, given that the mass of the crate is 32 kg and the coefficient of static friction between the crate and the floor is 0.57. 8. In Problem 7, find the acceleration of the crate if the applied force is 330 N and the coefficient of kinetic friction is 0.45.
9. A 45-kg crate is placed on an inclined ramp. When the angle the ramp makes with the horizontal is increased to 23, the crate begins to slide downward. (a) What is the coefficient of static friction between the crate and the ramp? (b) At what angle does the crate begin to slide if its mass is doubled? 10. A person places a cup of coffee on the roof of her car while she dashes back into the house for a forgotten item. When she returns to the car, she hops in and takes off with the coffee cup still on the roof. (a) If the coefficient of static friction between the coffee cup and the roof of the car is 0.24, what is the maximum acceleration the car can have without causing the cup to slide? Ignore the effects of air resistance. (b) What is the smallest amount of time in which the person can accelerate the car from rest to 15 m/s and still keep the coffee cup on the roof?
12. At the local hockey rink, a puck with a mass of 0.12 kg is given an initial speed of 5.3 m/s. (a) If the coefficient of kinetic friction between the ice and the puck is 0.11, what distance d does the puck slide before coming to rest? (b) How much KE does the puck lose while coming to a stop? (c) How much work does the rough ice do on the puck in bringing it to a stop? (d) If the mass of the puck is doubled, does the frictional force F exerted on the puck increase, decrease, or stay the same? Explain. (e) Does the stopping distance of the puck increase, decrease, or stay the same when its mass is doubled? Explain. 13. A block of mass m = 1.95 kg slides with an initial speed v o = 4.33 m/sec on a smooth (means frictionless), horizontal surface. The block now encounters a rough patch with a coefficient of kinetic friction given by µ k = 0.260 The rough patch extends for a distance d = 0.125 meters, after which the surface is again frictionless. (a) What is the acceleration of the block when it is in the rough patch? (b) What is the speed v f of the block when it exits the rough patch? (c) Calculate the work done by friction as the block slid across the table. 34. You want to nail a 1.3-kg board onto the wall of a barn. To position the board before nailing, you push it against the wall with a horizontal force F to keep it from sliding to the ground. (a) If the coefficient of static friction between the board and the wall is 0.86, what is the least force you can apply and still hold the board in place? (b) What happens to the force of static friction if you push against the wall with a force greater than that found in part (a)?
55. Find the coefficient of kinetic friction between a 3.85-kg block and the horizontal surface on which it rests if a 85.0-N/m spring must be stretched by 6.20 cm to pull it with constant speed. Assume that the spring pulls in the horizontal direction. 56. A child goes down a playground slide that is inclined at an angle of 27.5 below the horizontal. Find the acceleration of the child given that the coefficient of kinetic friction between the child and the slide is 0.415. 60. A 12-g coin slides upward on a surface that is inclined at an angle of 15 above the horizontal. The coefficient of kinetic friction between the coin and the surface is 0.23; the coefficient of static friction is 0.31. Find the magnitude and direction of the force of friction (a) when the coin is sliding and (b) after it comes to rest. 61. In Problem 60, the angle of the incline is increased to 25. Find the magnitude and direction of the force of friction when the coin is (a) sliding upward and (b) sliding downward.
66. 65. The system shown below is in equilibrium. (a) Find the frictional force exerted on block A given that the mass of block A is 8.50 kg, the mass of block B is 2.25 kg, and the coefficient of static friction between block A and the surface on which it rests is 0.320. (b) If the mass of block A is doubled, does the frictional force exerted on it increase, decrease, or stay the same? Explain.
74. At the airport, you pull a 18-kg suitcase across the floor with a strap that is at an angle of 45 above the horizontal. Find the normal force and the tension in the strap, given that the suitcase moves with constant speed and that the coefficient of kinetic friction between the suitcase and the floor is 0.38.